Unit of true strain:

True strain is a measure of the deformation or elongation experienced by a material when subjected to an external force. It is defined as the natural logarithm of the ratio of the final length of a material to its original length. Since it is a logarithmic function, true strain is dimensionless and does not have any units.

Explanation:

True strain is a more accurate measure of deformation compared to engineering strain, especially in cases where the material undergoes significant elongation or compression. It takes into account the change in length of the material throughout the deformation process, rather than just the initial and final lengths.

When a material is subjected to an external force, it undergoes plastic deformation, which causes changes in its dimensions. The true strain accounts for these changes by considering the instantaneous and incremental changes in length as the material deforms.

The true strain is calculated using the formula:

ε_t = ln(L_f / L_0)

Where:
ε_t = True strain
L_f = Final length of the material
L_0 = Original length of the material

Since the natural logarithm is used in the formula, the true strain is dimensionless. It is expressed as a ratio of lengths, but without any specific units.

The advantage of using a dimensionless measure like true strain is that it allows for direct comparison between materials regardless of their original dimensions or units. It also simplifies calculations and analysis, as there is no need to convert between different unit systems.

In conclusion, the unit of true strain is dimensionless. It is expressed as a ratio of lengths, but without any specific units. The true strain provides a more accurate measure of deformation by considering the instantaneous and incremental changes in length experienced by a material during deformation.